Varnish, Shellac or Varathane?

We moved into a house where the floors are covered in varnish, shellac, or varathane. We do not know which was applied, but some of it is now flaking off. How can we find out which one was applied, and what can be done to repair the floors?

Apply to the floor some old fingernail polish remover that contains acetone. If it dissolves, then you have old varnish on the floor. If it does not dissolve, then the floor is covered in varathane or urethane. If it is varathane or urethane you will have to use sandpaper or paint stripper to get it off. If it is varnish, you can apply a furniture restorer to it without having to first strip it off. The restorer will dissolve the existing varnish and cover it nicely.